Posted by
John Kennison on
URL: http://friam.383.s1.nabble.com/Wittgenstein-tp1133169p1307036.html
Glen and Phil,
Thanks for your comments. I think I've reached the limits of what I might learn for now. When it comes to the foundations of math, I have trouble trying to get very far beyond the feelings and impressions I have when doing math. It feels as if mathematical objects have some kind of independent existence --and I don't know what to say beyond that. When I construct a proof, I see myself as arranging symbols according to formal rules (although the written version of the proof is in a shorthand as a full formal proof of any complexity would be unreadable). The Intuitionist idea (as I understand it) that math takes place inside the human brain feels correct too, but I don't agree with most of the conclusions that Intuitionists derive from this. All of these views co-exist rather peacefully in my more or less unexamined thoughts about what math is
---John
________________________________________
From:
[hidden email] [
[hidden email]] On Behalf Of glen e. p. ropella [
[hidden email]]
Sent: Wednesday, October 08, 2008 7:42 AM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Wittgenstein
Thus spake John F. Kennison circa 10/07/2008 06:32 PM:
> I see your
> interpretation of Wittgenstein's statements as his way of saying that
> mathematical argument does not do a good or reliable job of
> establishing truth. Am I characterizing your position correctly?
Well, I think W. was arguing against Platonism in mathematics. That's
subtly different from saying that math argument does not do a good or
reliable job of establishing "truth" (i.e. reality)[*]. But, basically,
yes. I think if pressed, W. would agree with your statement. He would
actually go far far beyond your statement and say that math is a
pathological perversion of thought. Indeed, it is a dangerous and
misleading perversion (though it may be effective in highly skilled
hands). The point W was trying to make was that to fixate on math and
elevate it to science is a grave mistake. Doing so will prevent you
from learning how the world really works.
To be clear, my position is different from W's. I think math is related
to reality because we (biological animals) invented math as a way to
help us navigate the world. I think there are both evolutionary and
psychological justifications for the relationship between reality and math.
[*] We have to be careful to distinguish between the validity of a
statement and the soundness of a statement. Validity has to do with
whether or not a statement is mathematically well-formed. If it is (and
if the language is complete), then it is either true or false. But just
because a statement is true doesn't mean it's sound ... i.e. backed up
by data taken from reality.
--
glen e. p. ropella, 971-219-3846,
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